Optical modulator with automatic bias correction

ABSTRACT

An optical modulator uses an optoelectronic phase comparator configured to provide, in the form of an electrical signal, a measure of a phase difference between two optical waves. The phase comparator includes an optical directional coupler having two coupled channels respectively defining two optical inputs for receiving the two optical waves to be compared. Two photodiodes are configured to respectively receive the optical output powers of the two channels of the directional coupler. An electrical circuit is configured to supply, as a measure of the optical phase shift, an electrical signal proportional to the difference between the electrical signals produced by the two photodiodes.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.15/468,831, filed on Mar. 24, 2017, now U.S. patent Ser. No. 10/234,703which is a divisional of U.S. patent application Ser. No. 15/163,178,filed on May 24, 2016, now U.S. Pat. No. 9,638,940, which is adivisional of U.S. Patent application Ser. No. 14/182,03% filed Feb. 17,2014, now U.S. Pat. No. 9,372,354, which application claims the benefitof French Patent Application No. 1351675, filed on Feb. 26, 2013, whichapplications are hereby incorporated herein by reference.

FIELD OF THE INVENTION

The invention relates to an optical modulator according to theMach-Zehnder Interferometer principle, and, more particularly, to thestabilization of the operating point of the modulator with respect tovariations of various external parameters.

BACKGROUND

FIG. 1 schematically shows an example of an optical modulator ofMach-Zehnder interferometer type, often called an MZI modulator. Anoptical wave having a power P0 arrives through a waveguide to an opticalseparation unit S1, a Y-separator here. The initial wave is separatedinto two half-power waves, respectively guided in two parallel, upperand lower branches. Each branch comprises, in series, a fast opticalphase modulation diode HSPM (“High Speed Phase Modulator”) and a slowoptical phase adjusting diode PINPM.

Each of the diodes HSPM and PINPM introduces an adjustable phase delayof the optical wave crossing the diode by producing electric charge inthe light path. The HSPM diode operates in reverse bias mode; electriccharge is pulled from the junction into the optical path by a junctiondepletion phenomenon, the junction being offset relative to the opticalpath. The diode PINPM operates in a forward bias mode. It includes aP-I-N junction, the intrinsic region of which is in the light path andreceives electrical charge by an injection phenomenon.

The diode PINPM reacts slowly to changes in its bias, but it has a widerange of phase delay adjustment—it is used to adjust an optimalquiescent phase delay in the branch. Thus, the diodes PINPM of the twobranches (PINPM1 and PINPM2) receive respective constant bias currentsdepending on the quiescent phase delays to be introduced in the twobranches.

The diode HSPM reacts quickly, but has a low phase modulationamplitude—it is used to modulate the phase delay with a digital signalto be transmitted around the quiescent phase delay established by thediode PINPM. Thus, the diodes HSPM of the two branches (HSPM1 and HSPM2)receive voltage signals that are modulated, based on the digital signalto be transmitted, between 0 and a positive value Vb. The voltagesignals applied to the diodes HSPM1 and HSPM2 are complementary so as toproduce a differential effect in the two branches.

The two branches reach an optical junction unit J1, here a directionalcoupler. The optical waves incident on the two channels of coupler J1are shifted by 180° at rest, whereby, in the case of a symmetriccoupler, the optical power P1, P2 delivered by each channel of thecoupler J1 is 50% of the input power P0 of the modulator, the absorptionlosses in the branches being neglected. Diodes PINPM1 and PINPM2 arebiased by different currents. For example, the diode PINPM2 is biased bya zero current introducing theoretically a zero phase delay, and thediode PINPM1 is biased by a current Ib selected to introduce a phasedelay of 180°.

FIG. 2 is a diagram illustrating the variation of the transmission rateP1/P0 of the modulator, measured at the output of the upper channel ofthe coupler J1, as a function of the phase difference between the wavesat the inputs of the coupler J1. The transmission rate P2/P0, not shown,at the output of the lower channel, varies inversely.

The initial phase shift of 180° introduced by the diodes PINPM placesthe operating point of the modulator at the inflection point of asinusoid, in a region where the linearity is best and the slope issteepest. The diode HSPM1 causes the phase to vary in a range above180°, while the diode HSPM2 causes the phase to vary symmetrically in arange below 180°. By limiting the amplitude of these ranges, thecorresponding change in the rate of transmission may be almost linear.For the transmission of digital signals, the linearity is lessimportant, but it may be preferable that the behavior of the modulatorremains balanced, which is the case under the conditions of FIG. 2.

In practice, the bias currents of the diodes PINPM are individuallyadjusted for obtaining the desired quiescent conditions. However, adrift of the quiescent conditions may be noticeable, particularly as afunction of temperature.

SUMMARY

Thus there is a need for compensating the drift in the quiescentconditions of an MZI modulator. It may also be desirable to avoidindividual adjustment of the bias currents of modulators in a productionenvironment.

These needs are addressed by an optoelectronic phase comparatorconfigured to provide, in the form of an electrical signal, a measure ofa phase difference between two optical waves. The phase comparatorcomprises an optical directional coupler having two coupled channelsrespectively defining two optical inputs for receiving the two opticalwaves to be compared. Two photodiodes are configured to respectivelyreceive the optical output powers of the two channels of the directionalcoupler. An electrical circuit is configured to supply, as a measure ofthe optical phase shift, an electrical signal proportional to thedifference between the electrical signals produced by the twophotodiodes.

An MZI optical modulator may thus comprise an optical separation unitfor separating an incoming optical wave into a first and a secondoptical wave; a first and a second optical phase adjusting diodeinserted respectively in the paths of the first and second opticalwaves; and a first and a second optical directional coupler, each havingfirst and second coupled channels, the first channels being insertedrespectively in the paths of the first and second optical waves. The MZIoptical modulator may also include an optoelectronic phase comparator asmentioned above, having its optical inputs respectively connected to thesecond channels of the first and second directional couplers; and acircuit for electrically biasing the phase adjusting diodes, connectedin a control loop with the optoelectronic phase comparator.

According to an embodiment, the optical modulator comprises, between oneof the optical inputs of the phase comparator and the secondcorresponding channel of the first or second directional coupler, anintermediate directional coupler connected such that the phasedifference between the two optical waves incident on the inputs of thephase comparator is equal to 180°.

According to an embodiment, the optical modulator comprises an opticalwave junction unit having two inputs connected respectively to theoutputs of the first channels of the first and second directionalcouplers; and a first and a second optical phase modulation dioderespectively inserted in the connections between the junction unit andthe first and second directional couplers.

According to an embodiment, the separation unit and the junction unitare directional couplers, and the first and second phase adjustmentdiodes are biased so that they introduce a 90° phase delay one relativeto the other.

According to an embodiment, the separation unit is a directionalcoupler, the junction unit is a Y-combiner, and the first and secondphase adjustment diodes are biased to apply the same phase delay.

BRIEF DESCRIPTION OF THE DRAWINGS

Other advantages and features will become more clearly apparent from thefollowing description of particular embodiments provided for exemplarypurposes only and represented in the appended drawings, in which:

FIG. 1, previously described, schematically shows an exemplaryMach-Zehnder interferometer (MZI) modulator as in the prior art.

FIG. 2 is a graph illustrating the transmission rate of the modulator ofFIG. 1 as a function of the phase difference between the optical wavesof the two branches.

FIGS. 3A through 3D represent different configurations of an MZImodulator combining different types of optical separation and junctionunits according to the invention.

FIG. 4 shows an embodiment of an optoelectronic regulation circuitadapted to a first MZI modulator configuration according to theinvention.

FIG. 5 shows an alternative embodiment of the optoelectronic regulationcircuit adapted to another MZI modulator configuration according to theinvention.

FIG. 6 shows a detailed example of an optoelectronic regulation circuitaccording to the invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS

A P-I-N diode of an MZI modulator, even if its bias current is zero,causes a nonzero optical phase delay, a residual phase shift. Thisresidual phase shift depends on the characteristics obtained aftermanufacture, such as doping and dimensions. If the two PIN diodes of themodulator could be matched, they would provide the same residual phaseshift, which would be offset by the differential structure of themodulator. However, the diodes PINPM, which are formed in opticalwaveguides, are large compared to diodes used for plain electronicfunctions, and located far apart from each other at the scale of asemiconductor chip. As a result, it is difficult to match these“optical” diodes, and unpredictable offsets that are too great to beneglected are generally observed between the residual phase shifts ofthe two diodes PINPM.

Despite an accurate adjustment of the bias currents, even in modulatorconfigurations where the two diodes PINPM may have the same phasesetting, the quiescent conditions drift with temperature. This drift maybe explained by the fact that the rate of change of the phase shift as afunction of temperature depends on the operating conditions of the diodePINPM. These operating conditions are generally not identical initiallyfor the two diodes, whereby the phase shifts of the two diodes divergewhen the temperature varies.

The HSPM diodes are also subject to difficulties in matching, but theirstructure is inherently less sensitive to variability of manufacturingprocesses. It is noted that the offset between the residual phase shiftsof the two HSPM diodes, even after thermal drift, may remain withinacceptable limits to be neglected.

FIGS. 3A through 3D show configurations of MZI modulators differing bycombinations of separation and junction units requiring different biasconditions for the diodes PINPM. The structures of the two branches ofthe modulators are unchanged from FIG. 1.

FIG. 3A corresponds to the configuration of FIG. 1, already described.The separation unit S1 is a Y-separator and the junction unit J1 is asymmetric directional coupler. Separator S1 maintains the phase of theinput optical wave on both outputs, whereas the coupler J1 requires aphase difference of 180° to be in the center of its dynamic range, thedesired quiescent condition. Thus, diodes PINPM1 and PINPM2 are biasedto introduce an initial phase shift of 180° between the inputs of thecoupler J1.

The two waves exiting the coupler J1 are in phase quadrature, but theirphase difference with respect to the input waves is variable dependingon the characteristics of the input waves.

In FIG. 3B, the output directional coupler J1 has been replaced by aY-combiner J2. Such a combiner transmits 50% of the optical power whenthe waves at its two inputs are in phase quadrature. The two wavesarriving at the diodes PINPM being in phase, the diodes PINPM are biasedto introduce the desired phase difference of 90° between the two waves.E.g. the diode PINPM1 is biased to introduce a phase delay of 90° andthe diode PINPM2 receives a zero current, corresponding theoretically toa null phase delay. In practice, the diode PINPM2 introduces a residualphase delay at zero bias current, which is difficult to predict, forexample 1°. In that case, the diode PINPM1 is biased for introducing aphase delay of 90+1=91°.

The configuration of FIG. 3B may be preferred to that of FIG. 3A,because the diode PINPM1 causes less absorption losses than in FIG. 3A.Indeed, a greater phase delay is obtained in FIG. 3A by injecting morecharge in diode PINPM1, and absorption losses increase with the numberof charges.

In FIG. 3C, the Y-separator S1 of FIG. 3A has been replaced by asymmetrical directional coupler S2. The input optical wave is applied toone of the channels of the coupler, for example the lower one. In thatcase, the wave exiting the upper channel of the coupler is delayed by90° relative to the wave exiting the lower channel. The output couplerJ1 requiring a phase difference of 180° to operate in the desiredquiescent conditions, it is sufficient that the diode PINPM1 introduce aphase delay of 90° that is added to the delay of 90° introduced by theupper channel of the input coupler S2.

The absorption losses of the configuration of FIG. 3C are similar tothose of FIG. 3B.

In FIG. 3D, the output directional coupler J1 of FIG. 3C has beenreplaced by a Y-combiner J2. The input coupler S2 directly produces thephase quadrature desired for the quiescent conditions, between the wavesinput to the combiner J2. Thus, the diodes PINPM need not introduceadditional phase delay. In this case, the two diodes PINPM may be biasedat zero current, in theory. This configuration therefore provides thebest performance in terms of absorption losses.

Because the two diodes PINPM operate in similar conditions, thisconfiguration also offers the best performance in terms of thermaldrift.

In practice, the diode PINPM having the highest residual phase delay maybe biased at zero current, while the other diode PINPM is biased with acurrent sufficient to balance the residual phase delay. As it isdifficult to know in advance which of the two diodes PINPM has thehighest residual phase delay, it is preferred to bias both diodes withnon-zero currents, one fixed and one adjustable.

FIG. 4 shows an embodiment of an optoelectronic circuit for regulatingthe quiescent conditions of an MZI modulator. The MZI modulator has aconfiguration similar to that of FIG. 3D. With respect to FIGS. 3A to3D, the positions of the diodes PINPM have been interchanged with thoseof the HSPM diodes, so that the diodes PINPM are the first elements inthe two branches of the modulator, and are part of a control loop. TheHSPM diodes are not included in the loop—as mentioned earlier, thedrifts of the HSPM diodes may be neglected.

The optoelectronic regulation circuit, whose principles may be appliedto various MZI modulator configurations, such as those illustrated inFIGS. 3A to 3D, measures the optical phase difference between the wavesin the two branches of the modulator, and provides the error relative toa desired value in the form of optical power received by photodiodesPD1, PD2. The electrical signals provided by the photodiodes areexploited to vary the bias currents of the diodes PINPM in a directiontending to reduce the error.

The measurement of the phase difference may be achieved using asymmetrical optical directional coupler DC0 receiving, on its twochannels, optical waves derived from the two branches of the modulator.The paths of the derived optical waves are configured so that the phasedifference at the input of the coupler DC0 equals 180° when the phasedifference between the derived optical waves corresponds to that desiredat the input of the junction unit. Under these conditions, the couplerDC0 outputs at each of its channels 50% of the total optical powerreceived. If the phase difference is not equal to 180°, one of thechannels provides more than 50% of the power, while the other channelprovides the complement. The optical waves at the outputs of the twochannels of the coupler are provided to two respective photodiodes PD1,PD2. Thus, the difference between the electrical signals generated bythe photodiodes represents the optical phase error.

In FIG. 4, more specifically, the optical outputs of diodes PINPM1 andPINPM2 are provided to the first channels of two respective asymmetricdirectional couplers DC1 and DC2. The outputs of these first channelsare provided to diodes HSPM1 and HSPM2 respectively.

The couplers DC1 and DC2 are asymmetrical in that the optical powerreceived in the first channel is distributed asymmetrically between theoutputs of the first and second channels, for example 98% at the outputof the first channel, and 2% at the output of the second channel. Thefraction of the output power in the second channel is chosen to bedetectable by a photodiode in good conditions.

The optical waves output by the second channels of the couplers DC1 andDC2 have respective phase delays of 180° and 90° relative to the opticalwave input to the modulator (each of the couplers DC1 and DC2 introducesa phase delay of 90° as the wave passes from the first channel to thesecond). The phase difference between these waves is thus 90° while thecoupler/comparator DC0 requires 180°. A symmetrical directional couplerDC3 is provided to add the missing 90° phase delay to the 180° opticalwave. The coupler DC3 receives in its first channel the 180° wave andprovides a 270° wave from its second channel to the upper channel ofcoupler/comparator DC0.

A directional coupler DC4 is provided to equalize the optical pathsleading to the coupler/comparator DC0. Its first channel connects thecoupler DC2 to the lower channel of the coupler DC0, without introducinga phase delay.

The outputs of the first and second channels of the coupler/comparatorDC0 are respectively sensed by the photodiodes PD1 and PD2. Thesephotodiodes are part of an electrical control circuit 10 configured toadjust the bias currents of the diodes PINPM according to the differencebetween the sensed optical powers. In this modulator configuration, thebias currents are substantially the same, since the diodes PINPM aredesigned to introduce the same phase delay (as close to 0° as possible.)

The regulator circuit of FIG. 4 is also usable, as is, in the modulatorconfiguration of FIG. 3B.

FIG. 5 shows an alternative of the optoelectronic regulation circuit,integrated with an MZI modulator of the type of FIG. 3C. The sameelements as in FIG. 4 are designated by the same references. The diodePINPM1 is biased here for introducing a phase delay of 90°, so that thesecond channel of the coupler DC1 provides an optical wave delayed by270°. The second channel of the coupler DC2 still provides a wavedelayed by 90°. The phase difference between these waves is 180°,whereby the two waves may be directly applied to the inputs of thecoupler/comparator DC0.

The configuration of FIG. 5 is simpler than that of FIG. 4 in that ituses two directional couplers less.

The regulator circuit FIG. 5 is also usable, as is, in the modulatorconfiguration of FIG. 3A.

FIG. 6 shows a detailed example of electronic circuitry of theoptoelectronic regulation circuit 10. The photodiodes PD1 and PD2 arereverse biased by two resistors R1 and R2. The cathodes of diodes PD1and PD2 are connected respectively to a non-inverting input and aninverting input of a differential transconductance amplifier 20. Thediodes PINPM1 and PINPM2 are forward biased by respective constantcurrent sources Ib1 and Ib2. The anodes of diodes PINPM1 and PINPM2 areconnected to forward and reverse outputs of the amplifier 20.

The currents Ib1 and Ib2 are set by design to the typical valuesrequired to introduce the quiescent phase difference corresponding tothe modulator configuration (180° for FIG. 3A, 90° for FIGS. 3B and 3C,and 0° for FIG. 3D). In theory, one of the currents (Ib2) may be zero.In practice, the two currents are non-zero, so that each has a margin ofadjustment. Current Ib2 is selected, for example, to introduce a phasedelay of 5°. Then, the current Ib1 is selected to introduce a phasedelay of 185° in FIG. 3A, 95° in FIGS. 3B and 3C, and 5° in FIG. 3D.

When the phase difference between the input waves of coupler/comparatorDC0 is 180°, each of the photodiodes PD1 and PD2 receives the sameoptical power, 50% of the power received by the coupler/comparator DC0.If the photodiodes are matched, which is easier to achieve than fordiodes PINPM, their cathode voltages stand at identical values. Thus,the amplifier 20 sees a zero input voltage and does not influence thebias currents of the diodes PINPM.

If the phase difference between the input waves of coupler/comparatorDC0 drops below 180°, it means that the delay introduced by the diodePINPM1 decreases or the delay introduced by the diode PINPM2 increases.The optical power received by photodiode PD1 increases, and the opticalpower received by the photodiode PD2 decreases. The cathode voltage ofthe photodiode PD1 increases and that of the photodiode PD2 decreases.The amplifier 20 sees its differential input become positive—it injectsa proportional current in the diode PINPM1 and subtracts a proportionalcurrent from the diode PINPM2. The diode PINPM1 increases its phasedelay while the diode PINPM2 decreases its phase delay.

A symmetrical behavior is obtained when the phase shift between thewaves becomes greater than 180°.

An automatic correction is thus obtained for the quiescent phase errorsin the modulator. This correction is independent of the nature of theerror—the error may be due to a temperature drift, a poor matchingbetween the diodes PINPM, a poor initial choice of the bias currents, orany other cause. The accuracy of the correction depends on the open loopgain of the control loop, which may be easily adjusted by way ofamplifier 20.

The accuracy also depends on the parasitic offset referred to the inputof the amplifier, caused for instance by a mismatch between thephotodiodes or a lack of precision in the coupling coefficient of eachof couplers DC0, DC1 and DC2. Such an offset may be compensatedelectrically by techniques known in the field of differentialamplifiers.

What is claimed is:
 1. A method, comprising: adjusting, using a firstphase modulator, a quiescent phase of a first optical signal in a firstbranch of a modulator based on a first bias current provided to thefirst phase modulator; adjusting, using a second phase modulator, aquiescent phase of a second optical signal in a second branch of themodulator based on a second bias current provided to the second phasemodulator; generating a first input signal and a second input signalbased on the first optical signal and the second optical signal,respectively, wherein a phase of the first input signal is indicative ofthe quiescent phase of the first optical signal, and wherein a phase ofthe second input signal is indicative of the quiescent phase of a secondoptical signal; providing the first input signal and the second inputsignal to an optical directional coupler; generating a first outputsignal and a second output signal at output terminals of the opticaldirectional coupler; and adjusting, using a pair of photodiodes, thefirst bias current and the second bias current based on an optical phasedifference between the first input signal and the second input signal inaccordance with the first output signal and the second output signal,respectively, wherein the adjusting reduces a phase difference betweenthe quiescent phase of the first optical signal and the quiescent phaseof the second optical signal.
 2. The method of claim 1, wherein at leastone of the first phase modulator or the second phase modulator comprisesa Mach-Zehnder type phase modulator.
 3. The method of claim 1, whereinthe first phase modulator and the second phase modulator are configuredto operate in a forward biased configuration.
 4. The method of claim 1,wherein the first phase modulator and the second phase modulator areconfigured to operate in a reverse biased configuration.
 5. The methodof claim 1, wherein a difference in power between the first outputsignal and the second output signal is indicative of the optical phasedifference between the first input signal and the second input signal.6. The method of claim 1, further comprising separating an incomingoptical wave into the first optical signal and the second opticalsignal.
 7. The method of claim 1, wherein each of the first bias currentand the second bias current is adjusted based on a quiescent phasedifference between an optical signal across a respective one of themodulator branches.
 8. The method of claim 1, further comprising havinga system comprising the first phase modulator, the second phasemodulator, the optical directional coupler, and the pair of photodiodes,wherein a difference in power between the first output signal and thesecond output signal is indicative of the optical phase differencebetween the first input signal and the second input signal.
 9. Themethod of claim 8, wherein the optical directional coupler is configuredto receive the first input signal and the second input signal beforegenerating the first output signal and the second output signal.
 10. Themethod of claim 8, further comprising having an optical separation unitconfigured to separate an incoming optical wave into the first opticalsignal and the second optical signal.
 11. The method of claim 8, whereineach of the first bias current and the second bias current is adjustedbased on a quiescent phase difference between an optical signal across arespective one of the modulator branches.
 12. A method, comprising:adjusting, using a first phase modulator, a quiescent phase of a firstoptical signal in a first branch of a modulator based on a first biascurrent provided to the first phase modulator; adjusting, using a secondphase modulator, a quiescent phase of a second optical signal in asecond branch of the modulator based on a second bias current providedto the second phase modulator, wherein the first phase modulator and thesecond phase modulator are configured to operate in a forward biasedconfiguration; generating a first input signal and a second input signalbased on the first optical signal and the second optical signal,respectively, wherein a phase of the first input signal is indicative ofthe quiescent phase of the first optical signal, and wherein a phase ofthe second input signal is indicative of the quiescent phase of a secondoptical signal; providing the first input signal and the second inputsignal to an optical directional coupler; generating a first outputsignal and a second output signal at output terminals of the opticaldirectional coupler; and adjusting, using a pair of photodiodes, thefirst bias current and the second bias current based on an optical phasedifference between the first input signal and the second input signal inaccordance with the first output signal and the second output signal,respectively, wherein the adjusting reduces a phase difference betweenthe quiescent phase of the first optical signal and the quiescent phaseof the second optical signal.
 13. The method of claim 12, wherein adifference in power between the first output signal and the secondoutput signal is indicative of the optical phase difference between thefirst input signal and the second input signal.
 14. The method of claim12, further comprising separating an incoming optical wave into thefirst optical signal and the second optical signal.
 15. The method ofclaim 12, wherein at least one of the first phase modulator or thesecond phase modulator comprises a Mach-Zehnder type phase modulator.16. The method of claim 12, further comprising having a systemcomprising the first phase modulator, the second phase modulator, theoptical directional coupler, and the pair of photodiodes, wherein eachof the first bias current and the second bias current is adjusted basedon a quiescent phase difference between an optical signal across arespective one of the modulator branches.
 17. A method, comprising:adjusting, using a first phase modulator, a quiescent phase of a firstoptical signal in a first branch of a modulator based on a first biascurrent provided to the first phase modulator; adjusting, using a secondphase modulator, a quiescent phase of a second optical signal in asecond branch of the modulator based on a second bias current providedto the second phase modulator, wherein the first phase modulator and thesecond phase modulator are configured to operate in a reverse biasedconfiguration; generating a first input signal and a second input signalbased on the first optical signal and the second optical signal,respectively, wherein a phase of the first input signal is indicative ofthe quiescent phase of the first optical signal, and wherein a phase ofthe second input signal is indicative of the quiescent phase of a secondoptical signal; providing the first input signal and the second inputsignal to an optical directional coupler; generating a first outputsignal and a second output signal at output terminals of the opticaldirectional coupler; and adjusting, using a pair of photodiodes, thefirst bias current and the second bias current based on an optical phasedifference between the first input signal and the second input signal inaccordance with the first output signal and the second output signal,respectively, wherein the adjusting reduces a phase difference betweenthe quiescent phase of the first optical signal and the quiescent phaseof the second optical signal.
 18. The method of claim 17, wherein adifference in power between the first output signal and the secondoutput signal is indicative of the optical phase difference between thefirst input signal and the second input signal.
 19. The method of claim17, further comprising separating an incoming optical wave into thefirst optical signal and the second optical signal.
 20. The method ofclaim 17, wherein at least one of the first phase modulator or thesecond phase modulator comprises a Mach-Zehnder type phase modulator.